Gradient Structures from Classical to Quantum - Part 3 of 3

Explore the final lecture in a three-part series where Oliver Tse of Eindhoven University of Technology delves into gradient structures across classical and quantum domains. Recorded on March 14, 2025, at IPAM's Non-commutative Optimal Transport Tutorials at UCLA, this 77-minute presentation completes the exploration of how gradient flows unify concepts from thermodynamics, optimal transport, and quantum mechanics. The lecture builds upon previous sessions to examine quantum analogs of gradient flows, their applications in open quantum systems, quantum entropy dissipation, and non-commutative transport. Gain insights into the emerging mathematical structures that bridge classical and quantum dynamics, offering a comprehensive understanding of how variational principles govern evolution in both realms. Part of IPAM's long program on Non-commutative Optimal Transport.